The constant-roll inflation in the context of Galilean inflation or G-inflation is analyzed. By considering some coupling function G(ϕ, χ) associated with the model of G-inflation, we find different inflationary solutions in the context of the constant roll scenario. In order to present an analytical discussion, we work with two specific cases of the general function G(ϕ, χ) ∝ g(ϕ) χ n , e.g. (i) G(ϕ, χ) ∝ ϕ when g(ϕ) = ϕ and n = 0 and (ii) G(ϕ, χ) ∝ √χ when g(ϕ) = constant and n = 1/2. Also, we introduce a new function G(ϕ, χ) associated with both variables ϕ and χ. We reconstruct the potential of the scalar field for the considered cases of the function G in the context of the constant-roll approach and then we study the corresponding cosmological perturbations of the model. Eventually, we use the recent observations datasets in order to constrain the parameter-space of the model.
